The present invention relates generally to the measurement of radioactivity and, more particularly, to the measurement of the radioactivity of a sample in an environment in which there is a significant background level of radiation not attributable to the sample itself. Many commercial radiation counters include a feature which allows for the automatic subtraction of a predetermined quantity, representing background radiation, from the measured radiations rate of the sample, to obtain a radiation rate attributable to the sample alone. However, as will be explained, these instruments provide a false indication of the actual statistical error limits relating to the radiation rate of the sample alone.
In general, instruments for the measurement of radioactivity operate by detecting discrete radiations, and accumulating a count of the detected radiations. Depending on the decay characteristics of the sample being tested, and on the particular experiment being conducted, the instrument will usually be adjusted to detect radiation with energies falling within preselected energy limits which define an energy level range or "window". Since the process of radioactive decay is a random one, the accuracy of any measurement of radioactivity, in counts per unit time, will depend upon the number of counts detected during the course of the measurement. It will be apparent that, if a large number of counts is accumulated over a relatively long testing period, the counts-per-unit-time measurement obtained will be more accurate than if a smaller number of counts were measured over a correspondingly shorter period of time.
A statistical parameter which is often used in radiation measurement to indicate the reliability of a measurement of radiation, is the standard deviation, indicated by the symbol .sigma.. As will be further explained, in some cases it is desirable to express the reliability of a measurement in terms of a multiple of the standard deviation, e.g. 2.sigma.. Hereinafter the terms "error value" and "+E" will be used to include standard deviation and multiples thereof. The value of the standard deviation for a number of counts N is given by the equation: EQU .+-. .sigma..sub.N = .+-. .sqroot.N . (1)
in percentage form, the standard deviation is given by: ##EQU1## The significance of the standard deviation is that, for a large number of measurements, there is a 68.3% probability that any equivalent measurement taken will be within .+-..sigma. of the mean value of the large number of measurements. In the measurement of radioactivity, each accumulated count essentially constitutes a new measurement. More specifically, each time a count is accumulated, it provides, together with all the preceding counts, a new basis for determining the radioactivity of the sample. Accordingly, after the accumulation of N counts, there is a 68.3% probability that a second measurement based on the accumulation of counts for the same time period will be within .+-..sigma..sub.N of the average value of radioactivity determined from the N counts. Stated another way, there is a 68.3% probability that the true radioactivity of the sample is within the range .+-..sigma..sub.N of the radioactivity determined from N counts.
As mentioned above, it is also common in the measurement of radioactivity to use twice the standard deviation, i.e., .+-.2.sigma., where this has the significance that 95.5% of the measured values will be within .+-.2.sigma. of the average value. The calculation of .+-.2.sigma. is performed in accordance with the equation: EQU .+-. 2.sigma..sub.N = .+-. 2 .sqroot.N , (3)
or, in percentage form: ##EQU2##
In many applications involving the measurement of radioactivity, it is extremely important that the range of possible errors in a measurement be known accurately. For example, one such application involves the use of radioactive isotopes as tracers in radioimmunoassay procedures for the measurement of concentration levels of specific antigens, antibodies or other substances in blood. A diagnosis of a patient's condition, based on the measurement of the radioactivity of these tracers in a blood sample, might well be an incorrect one if the range of possible error in the radiation count is not reliably known.
This problem is further compounded by the characteristic shape of a typical response curve relating the measured level of radioactivity to the concentration of some substance in the blood sample being measured. Complex chemical reactions are usually involved, and the concentration typically decreases with increasing radiation levels, and increases with decreasing radiation levels. More importantly, a small error in detected radiation at relatively low levels of radiation will, because of the slope of the curve, be reflected as a relatively larger error in estimated concentration. Accordingly, if the range of error in the radiation level is not accurately known, this inaccuracy is reflected in a still larger inaccuracy in the range of error in the concentration being monitored, and may thereby limit the reliability of clinical diagnosis for a patient.
As mentioned eariler, many commercial radiation counters are capable of automatically subtracting a preset quantity, indicative of a measured background level of radiation, from the measured radiation rate. Moreover, many instruments of this type will also calculate and display an error value, such as .+-..sigma. or .+-.2.sigma., for the count rate measured. However, in all such prior art instruments the error value presented to the user is derived only from the total actual number of counts measured, which, of course, in indicative of the level of radiation from both sample and background sources taken together. The error value computed in this manner, i.e., without reference to the error value relating to the measurement of background radiation alone, may be different from the true error value by a rather substantial factor, depending on the specific magnitudes of the sample and background radiation levels.